What do I think is difficult?
I first found the idea of a contrapositive difficult to understand. It just didn't make too much sense to me that P -> Q could be equivalent to ~Q -> ~P. I understood that it was a theorem, and I think that in a previous life I would have taken that to be true without blinking twice. But since I've been in this proofs class, I have learned to question thing and prove them to believe them.
It also didn't make sense that you could do a proof by contrapositive. I thought to myself, "How could you prove something to be true by only talking about their negations. With more practice, I believe I will become more comfortable with them.
What do I find interesting?
You know, I've done lots of math classes throughout my life. I've had lot of different tests in my life that have asked me to prove whether things are true or false. I've never done too well with these problems, mainly because I haven't known different ways to actually do these proofs.
Now, I've learned contrapositive, where I can prove something is true by proving the contrapositive. I also learned proof by cases. I feel that with learning these different ways to do proofs, I will be able to not only do better on tests, but to think through things and find out what is true and false by taking a step back and applying one of these different proving methods. I look forward to using these in homework and seeing how they work. I also look forward to learning other direct proving methods.
I first found the idea of a contrapositive difficult to understand. It just didn't make too much sense to me that P -> Q could be equivalent to ~Q -> ~P. I understood that it was a theorem, and I think that in a previous life I would have taken that to be true without blinking twice. But since I've been in this proofs class, I have learned to question thing and prove them to believe them.
It also didn't make sense that you could do a proof by contrapositive. I thought to myself, "How could you prove something to be true by only talking about their negations. With more practice, I believe I will become more comfortable with them.
What do I find interesting?
You know, I've done lots of math classes throughout my life. I've had lot of different tests in my life that have asked me to prove whether things are true or false. I've never done too well with these problems, mainly because I haven't known different ways to actually do these proofs.
Now, I've learned contrapositive, where I can prove something is true by proving the contrapositive. I also learned proof by cases. I feel that with learning these different ways to do proofs, I will be able to not only do better on tests, but to think through things and find out what is true and false by taking a step back and applying one of these different proving methods. I look forward to using these in homework and seeing how they work. I also look forward to learning other direct proving methods.
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